Croll was aware that the obliquity of earth's axis varied through time, but Leverrier's astronomical calculations only allowed Croll to include eccentricity and precession in his theory.
Milankovitch, on the other hand, benefited from innovations in astronomy that made it possible to incorporate changes in tilt into his calculations. Earth's axial tilt varies from 24.5 degrees to 22.1 degrees over the course of a 41,000-year cycle.
Changes in axial tilt affect the distribution of solar radiation received at the earth's surface. When the angle of tilt is low, polar regions receive less insolation. When the tilt is greater, the polar regions receive more insolation during the course of a year. Like precession and eccentricity, changes in tilt thus influence the relative strength of the seasons, but the effects of the tilt cycle
are particularly pronounced in the high latitudes where the great ice ages began.

With
Pilgrim's new calculations as his guide, Milankovitch embarked on an exhaustive series of calculations. Without a computer or even a calculator, the task was arduous indeed. While the calculations were complex, the reasoning behind them was quite
simple. Croll had argued that winter insolation was the key factor in understanding the ice ages, but Milankovitch thought that summer insolation was more important. During periods of lower summer temperatures, he reasoned, less of the previous
winter's snow would melt. Glaciation would soon begin after the snows of several winters piled up. Milankovitch set out to determine how variations in precession, eccentricity, and obliquity affected the amount of solar radiation received during the summer at particular latitudes.